Exploring Area, Perimeter, and Polynomial Factoring

A rectangular garden has a length of (x + 5) meters and a width of (x - 2) meters. What is the area of the garden in terms of x?

• x^2 + 3x + 10

• x^2 + 7x - 10

• x^2 - 3x - 10

• x^2 + 3x - 10

The perimeter of a square is represented by the polynomial 4s, where s is the length of a side. If the perimeter is 48 meters, what is the value of s?

• 14

• 16

• 12

• 10

A rectangular pool has a length of (2x + 3) meters and a width of (x + 1) meters. Factor the polynomial expression for the area of the pool.

• (2x + 3)(x - 1)

• (2x + 1)(x + 1)

• (2x + 3)(x + 1)

• (2x + 4)(x + 2)

A rectangular field has a length that is 3 meters longer than twice its width. If the width is represented by w, write a polynomial for the perimeter and find its value when w = 4 meters.

• 28

• 30

• 24

• 36

The area of a rectangular plot is given by the polynomial A = (x + 4)(x - 1). What is the width of the plot if the length is (x + 4)?

• x - 4

• x + 1

• x - 1

• x + 4

A triangular garden has a base of (x + 2) meters and a height of (2x - 3) meters. Write a polynomial expression for the area and find the area when x = 5.

• 15

• 24.5

• 20

• 30.5

The length of a rectangular room is represented by (x + 6) meters and the width by (x - 4) meters. What is the polynomial expression for the perimeter of the room?

• 4x + 8

• 2x + 12

• 4x + 4

• 6x - 8

A rectangular box has a length of (3x + 1) cm, a width of (x - 2) cm, and a height of (x + 3) cm. Write a polynomial for the volume and find the volume when x = 2.

• 8 cm³

• 12 cm³

• 0

• 6 cm³

The area of a rectangular garden is represented by the polynomial A = x^2 + 5x + 6. Factor this polynomial to find the dimensions of the garden.

• (x + 4) and (x + 2)

• (x + 5) and (x + 1)

• (x + 1) and (x + 6)

• The dimensions of the garden are (x + 2) and (x + 3).

A rectangular park has a length of (x + 10) meters and a width of (x - 5) meters. Graph the polynomial representing the area of the park and identify the x-intercepts.

• x-intercepts are x = 3 and x = -5.

• x-intercepts are x = 0 and x = 10.

• x-intercepts are x = 7 and x = -15.

• x-intercepts are x = 5 and x = -10.